Estimation, diagnostics, and extensions of nonparametric Hawkes processes with kernel functions

Abstract

The Hawkes self-exciting model has become one of the most popular point-process models in many research areas in the natural and social sciences because of its capacity for investigating the clustering effect and positive interactions among individual events/particles. This article discusses a general nonparametric framework for the estimation, extensions, and post-estimation diagnostics of Hawkes models, in which we use the kernel functions as the basic smoothing tool.